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/* Copyright (C) 1996 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by David Mosberger <davidm@cs.arizona.edu>, 1996.
Based on public-domain C source by Linus Torvalds.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
/* Faster 1 ulp error version by removing final last-bit fiddling, by
Joachim Wesner <joachim.wesner@frankfurt.netsurf.de>, July 1998 */
/* Modified and re-scheduled by Kazushige Goto <goto@statabo.rim.or.jp> */
/* Added exceptional handling by Kazushige Goto <goto@statabo.rim.or.jp> */
.set noat
.set noreorder
#ifdef __ELF__
.section .rodata
#else
.rdata
#endif
.align 5 # align to cache line
sqrtdata:
.long 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866
.long 0xf14a, 0x1091b, 0x11fcd, 0x13552, 0x14999, 0x15c98, 0x16e34, 0x17e5f
.long 0x18d03, 0x19a01, 0x1a545, 0x1ae8a, 0x1b5c4, 0x1bb01, 0x1bfde, 0x1c28d
.long 0x1c2de, 0x1c0db, 0x1ba73, 0x1b11c, 0x1a4b5, 0x1953d, 0x18266, 0x16be0
.long 0x1683e, 0x179d8, 0x18a4d, 0x19992, 0x1a789, 0x1b445, 0x1bf61, 0x1c989
.long 0x1d16d, 0x1d77b, 0x1dddf, 0x1e2ad, 0x1e5bf, 0x1e6e8, 0x1e654, 0x1e3cd
.long 0x1df2a, 0x1d635, 0x1cb16, 0x1be2c, 0x1ae4e, 0x19bde, 0x1868e, 0x16e2e
.long 0x1527f, 0x1334a, 0x11051, 0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd
.text
.globl sqrt
.align 5
.ent sqrt
sqrt:
.frame $30 , 32, $26
lda $30 , -32($30)
ldgp $29 , .-sqrt($27)
stt $f16, 0($30)
#ifdef PROF
lda $28, _mcount
jsr $28, ($28), _mcount
unop
unop
#endif
.prologue 1
lda $4 , sqrtdata # load base address into $4
ldah $2 , 0x5fe8
lda $18, 0x3fe0
lda $21, 0x7ff
ldq $3 , 0($30)
sll $18, 48, $18
lda $19, 0x4008
stq $18, 0x08($30) # 0.5
srl $3 , 33, $5
nop
subl $2 , $5 , $2
srl $3, 52, $20
srl $2 , 12, $1
ldt $f10, 0x08($30)
and $1 , 0xfc, $1
sll $19, 48, $19
addq $1 , $4 , $1
cmpteq $f31, $f31, $f11 # 2.0
and $21, $20, $23
addt $f10, $f10, $f12 # 0.5 + 0.5 = 1.0
ldl $1 , 0x0 ($1)
cmpeq $21, $23, $24
ldah $20,-0x10($19)
bne $24, $Inf_and_Nan
subl $2 , $1 , $2
stq $20, 0x10($30) # 3.0 - 4.0e-30
sll $2 , 32, $2
fblt $f16, $NaN
stq $2 , 0x18($30)
addt $f11, $f12, $f11 # $f11 = 3.0
beq $23, $SubNormal
nop
ldt $f13, 0x10($30)
ldt $f17, 0x18($30)
# $f10 : 0.5
# $f11 : 3.0
# $f12 : 1.0
# $f13 : 3.0(nearly)
mult $f16, $f17, $f18 # x * y
mult $f10, $f17, $f19 # 0.5 * y
mult $f18, $f17, $f21 # x * y * y
subt $f11, $f21, $f18 # 3. - x * y * y
mult $f19, $f18, $f17 # 0.5 * y * ( 3.0 - x * y * y)
mult $f16, $f17, $f18 # x * y
mult $f10, $f17, $f19 # 0.5 * y
mult $f18, $f17, $f18 # x * y * y
subt $f13, $f18, $f18 # (3.-4.0e-30) - x * y * y
mult $f19, $f18, $f17 # 0.5 * y * ( 3.0 - x * y * y)
mult $f16, $f17, $f18 # z = x * y
mult $f18, $f17, $f20 # z * y
mult $f10, $f18, $f19 # z * 0.5
subt $f12, $f20, $f20 # 1.0 - z * y
mult $f19, $f20, $f20 # z * 0.5 *(1.0-z*y)
addt $f18, $f20, $f0 # z +z * 0.5 *(1.0-z*y)
addq $30 , 32, $30
ret
.align 4
/* Exceptional Handling */
/* sqrt(NaN) = NaN, sqrt(+inf) = +inf, sqrt(-inf) = NaN */
$Inf_and_Nan:
lda $4, 0xfff0
sll $4, 48, $4
andnot $3, $4, $0
bne $0, $NaN
.align 4
$Infinity:
blt $3, $NaN
fmov $f16, $f0
addq $30 , 32, $30
ret
.align 4
$NaN:
lda $0, -1
stq $0, 0($30)
ldt $f0, 0($30)
addq $30 , 32, $30
ret
.align 4
$SubNormal:
lda $20, 0x7ff
ldah $23, 0x0010
sll $20, 52, $20
fbeq $f16, $Zero
andnot $3, $20, $22 # Extract floating point fp($22)
sll $23, 32, $23 # generate 0x00100000 00000000
lda $21, 2 # Clear exp part($21) and add 2
.align 4
zap $22, 0x0f, $25
bne $25, $SubNext1
sll $22, 20, $22
addq $21, 20, $21
zap $22, 0x0f, $25
bne $25, $SubNext1
sll $22, 20, $22
addq $21, 20, $21
.align 4
$SubNext1:
zap $22, 0x1f, $25
bne $25, $SubNext2
sll $22, 12, $22
addq $21, 12, $21
$SubNext2:
zap $22, 0x3f, $25
bne $25, $SubLoop
sll $22, 4, $22
addq $21, 4, $21
.align 4
$SubLoop:
sll $22, 1, $22 # fp << 1
and $22, $23, $0
addq $21, 1, $21 # exp++
beq $0, $SubLoop
.align 4
s4subq $23, $23, $25 # 0x0030....
addq $23, $23, $24 # 0x0020....
cmovlbc $21, $25, $24
andnot $22, $20, $22
or $22, $24, $3
srl $21, 1, $21 # exp >>= 1
stq $3, 0($30)
ldah $2 , 0x5fe8
srl $3 , 33, $5
subl $2 , $5 , $2
srl $2 , 12, $1
and $1 , 0xfc, $1
addq $1 , $4 , $1
ldl $1 , 0x0 ($1)
subl $2 , $1 , $2
sll $2 , 32, $2
stq $2 , 0x18($30)
ldt $f16, 0x00($30)
ldt $f13, 0x10($30)
ldt $f17, 0x18($30)
mult $f16, $f17, $f18 # x * y
mult $f10, $f17, $f19 # 0.5 * y
mult $f18, $f17, $f21 # x * y * y
subt $f11, $f21, $f18 # 3. - x * y * y
mult $f19, $f18, $f17 # 0.5 * y * ( 3.0 - x * y * y)
mult $f16, $f17, $f18 # x * y
lda $22, 1023
mult $f10, $f17, $f19 # 0.5 * y
subq $22, $21, $21
mult $f18, $f17, $f18 # x * y * y
sll $21, 52, $21
subt $f13, $f18, $f18 # (3.-4.0e-30) - x * y * y
mult $f19, $f18, $f17 # 0.5 * y * ( 3.0 - x * y * y)
stq $21, 0($30)
mult $f16, $f17, $f18 # z = x * y
mult $f18, $f17, $f20 # z * y
mult $f10, $f18, $f19 # z * 0.5
subt $f12, $f20, $f20 # 1.0 - z * y
ldt $f1, 0($30)
mult $f19, $f20, $f20 # z * 0.5 *(1.0-z*y)
addt $f18, $f20, $f0 # z +z * 0.5 *(1.0-z*y)
mult $f0, $f1, $f0
addq $30 , 32, $30
ret
.align 4
$Zero:
fmov $f16, $f0
addq $30 , 32, $30
ret
.end sqrt
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